Inverse problems aim to recover unknown signals from corrupted measurements, often under limited or unpaired data. In this talk, I will present two recent directions in Neural Optimal Transport motivated by inverse problems and function-space learning. First, I will introduce UOTIP, which formulates unpaired image inverse problems as an Unbalanced Optimal Transport map from noisy measurements to clean signals. By incorporating a likelihood-based cost, UOTIP admits a MAP-estimation interpretation, improves robustness to multi-level noise and class imbalance, and provides a theoretical guarantee for the existence and uniqueness of the transport map. Second, I will discuss HiSNOT, which extends Semi-dual Neural Optimal Transport to infinite-dimensional Hilbert spaces, providing a theoretical foundation for function-to-function transport maps relevant to Neural Operator learning. To address the spurious solution problem arising from the low-dimensional structure of functional data, HiSNOT employs principled Gaussian smoothing with provable convergence guarantees. Together, these works suggest a path toward extending Neural Optimal Transport from image inverse problems to stable operator learning in function spaces.

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(세미나 ZOOM 링크: https://cau.zoom.us/j/88050404196// 회의 ID: 880 5040 4196)